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Simulated Link Model: LRD Traffic 10  Internet traffic : known to be LRD with Hurst parameter value between 0.7 and 0.9.  REC for Hurst=0.75 is significantly higher than our 2-state MMPP model results.  We also observed that REC increases as Hurst value increases towards 0.9. DELAY – LRD/D/1 LOSS – LRD/D/1/K  Also looked at closed-loop traffic - many TCP flows - and observed similar trends.  We further looked at the case when Premium traffic is CBR and BE is TCP, and this increased REC further.

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Network Model Steps to calculate network REC (NREC): –Step 1: Construct the routing matrix R FxL based on shortest path Run Dijkstra’s algorithm on the topology matrices A NxN and W NxN –Step 2: Form the traffic vector Fx1 from T NxN –Step 3: Calculate the traffic load on each link: R T = Q –Step 4: Check the feasibility of the traffic load and routing For any link –If link capacity is less than the traffic load (e.g. C < Q) then update T accordingly and go to Step 2. –Step 5: Calculate the required per-link REC (i.e.  N -  D ) by using Q I as the traffic rate D for Ith link, and the performance goal p target or t target. Used Rocketfuel topologies for A NxN and W NxN. Used gravity model for T NxN. Made a look-up to the simulated link model results. 11

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NREC: Two ways to calculate Steps to calculate network REC (NREC) (cont’d): –Step 6: Calculate the NREC by averaging the per-link RECs from Step 5. We calculated NRECs for the Rocketfuel topologies: –Used the MMPP link model (a=0.5 and r=4) or the LRD link model (H=0.75) – Much more conservative than real or TCP traffic –Assumed K=100ms buffer time –Only report Sprintlink, as the other topologies gave higher REC values 12 total extra capacity needed on the whole network average extra capacity needed on each link

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NREC for Sprintlink: G2G Delay Solid lines are NREC I and dashed lines are NREC A 13 NREC can be much higher than 100% for a network operating with 60% utilization. 10ms queueing delay target for VoIP may require large REC values.

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NREC for Sprintlink: G2G Loss Solid lines are NREC I and dashed lines are NREC A 14 NREC can be much higher than 1000% even for a network operating with 40% utilization. 0.1% loss target may require large REC values.

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Summary A framework to study REC for delay or loss being the performance target. Link model –REC grows when: traffic becomes more bursty the utilization of the CoS link becomes higher the performance target becomes tighter the fraction g of the Premium class traffic becomes smaller –Closed-loop (e.g., TCP) or LRD traffic further increases REC Network model: –For legacy g2g performance targets, REC ranges from 50% to over 100% as g reduces below 0.5 and the utilization goes up to 60%. Future trends/work: –The performance targets will keep becoming tighter. REC is high perpetually – not just today, but in future also.. –The value of g is a crucial factor. Small g does not necessary favor a classless network. –Further research should estimate the actual costs of CoS and classless designs, as scheduling & management complexity need to be considered. 15